Solve for x (3x+6)/2-(7x-14)/3-(x+1)/9=0

$\frac{3 x + 6}{2} - \frac{7 x - 14}{3} - \frac{x + 1}{9} = 0$

Step 1

Simplify $\frac{3 x + 6}{2} - \frac{7 x - 14}{3} - \frac{x + 1}{9}$ .

Find the common denominator.

Multiply $\frac{3 x + 6}{2}$ by $\frac{9}{9}$ .

$\frac{3 x + 6}{2} \cdot \frac{9}{9} - \frac{7 x - 14}{3} - \frac{x + 1}{9} = 0$

Multiply $\frac{3 x + 6}{2}$ by $\frac{9}{9}$ .

$\frac{(3 x + 6) \cdot 9}{2 \cdot 9} - \frac{7 x - 14}{3} - \frac{x + 1}{9} = 0$

Multiply $\frac{7 x - 14}{3}$ by $\frac{6}{6}$ .

$\frac{(3 x + 6) \cdot 9}{2 \cdot 9} - (\frac{7 x - 14}{3} \cdot \frac{6}{6}) - \frac{x + 1}{9} = 0$

Multiply $\frac{7 x - 14}{3}$ by $\frac{6}{6}$ .

$\frac{(3 x + 6) \cdot 9}{2 \cdot 9} - \frac{(7 x - 14) \cdot 6}{3 \cdot 6} - \frac{x + 1}{9} = 0$

Multiply $\frac{x + 1}{9}$ by $\frac{2}{2}$ .

$\frac{(3 x + 6) \cdot 9}{2 \cdot 9} - \frac{(7 x - 14) \cdot 6}{3 \cdot 6} - (\frac{x + 1}{9} \cdot \frac{2}{2}) = 0$

Multiply $\frac{x + 1}{9}$ by $\frac{2}{2}$ .

$\frac{(3 x + 6) \cdot 9}{2 \cdot 9} - \frac{(7 x - 14) \cdot 6}{3 \cdot 6} - \frac{(x + 1) \cdot 2}{9 \cdot 2} = 0$

Multiply $2$ by $9$ .

$\frac{(3 x + 6) \cdot 9}{18} - \frac{(7 x - 14) \cdot 6}{3 \cdot 6} - \frac{(x + 1) \cdot 2}{9 \cdot 2} = 0$

Multiply $3$ by $6$ .

$\frac{(3 x + 6) \cdot 9}{18} - \frac{(7 x - 14) \cdot 6}{18} - \frac{(x + 1) \cdot 2}{9 \cdot 2} = 0$

Reorder the factors of $9 \cdot 2$ .

$\frac{(3 x + 6) \cdot 9}{18} - \frac{(7 x - 14) \cdot 6}{18} - \frac{(x + 1) \cdot 2}{2 \cdot 9} = 0$

Multiply $2$ by $9$ .

$\frac{(3 x + 6) \cdot 9}{18} - \frac{(7 x - 14) \cdot 6}{18} - \frac{(x + 1) \cdot 2}{18} = 0$

$\frac{(3 x + 6) \cdot 9}{18} - \frac{(7 x - 14) \cdot 6}{18} - \frac{(x + 1) \cdot 2}{18} = 0$

Combine the numerators over the common denominator.

$\frac{(3 x + 6) \cdot 9 - (7 x - 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Simplify each term.

Apply the distributive property.

$\frac{3 x \cdot 9 + 6 \cdot 9 - (7 x - 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Multiply $9$ by $3$ .

$\frac{27 x + 6 \cdot 9 - (7 x - 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Multiply $6$ by $9$ .

$\frac{27 x + 54 - (7 x - 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Apply the distributive property.

$\frac{27 x + 54 + (- (7 x) - - 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Multiply $7$ by $- 1$ .

$\frac{27 x + 54 + (- 7 x - - 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Multiply $- 1$ by $- 14$ .

$\frac{27 x + 54 + (- 7 x + 14) \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Apply the distributive property.

$\frac{27 x + 54 - 7 x \cdot 6 + 14 \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Multiply $6$ by $- 7$ .

$\frac{27 x + 54 - 42 x + 14 \cdot 6 - (x + 1) \cdot 2}{18} = 0$

Multiply $14$ by $6$ .

$\frac{27 x + 54 - 42 x + 84 - (x + 1) \cdot 2}{18} = 0$

Apply the distributive property.

$\frac{27 x + 54 - 42 x + 84 + (- x - 1 \cdot 1) \cdot 2}{18} = 0$

Multiply $- 1$ by $1$ .

$\frac{27 x + 54 - 42 x + 84 + (- x - 1) \cdot 2}{18} = 0$

Apply the distributive property.

$\frac{27 x + 54 - 42 x + 84 - x \cdot 2 - 1 \cdot 2}{18} = 0$

Multiply $2$ by $- 1$ .

$\frac{27 x + 54 - 42 x + 84 - 2 x - 1 \cdot 2}{18} = 0$

Multiply $- 1$ by $2$ .

$\frac{27 x + 54 - 42 x + 84 - 2 x - 2}{18} = 0$

$\frac{27 x + 54 - 42 x + 84 - 2 x - 2}{18} = 0$

Simplify terms.

Subtract $42 x$ from $27 x$ .

$\frac{- 15 x + 54 + 84 - 2 x - 2}{18} = 0$

Subtract $2 x$ from $- 15 x$ .

$\frac{- 17 x + 54 + 84 - 2}{18} = 0$

Simplify by adding and subtracting.

Add $54$ and $84$ .

$\frac{- 17 x + 138 - 2}{18} = 0$

Subtract $2$ from $138$ .

$\frac{- 17 x + 136}{18} = 0$

$\frac{- 17 x + 136}{18} = 0$

Factor $17$ out of $- 17 x + 136$ .

Factor $17$ out of $- 17 x$ .

$\frac{17 (- x) + 136}{18} = 0$

Factor $17$ out of $136$ .

$\frac{17 (- x) + 17 (8)}{18} = 0$

Factor $17$ out of $17 (- x) + 17 (8)$ .

$\frac{17 (- x + 8)}{18} = 0$

$\frac{17 (- x + 8)}{18} = 0$

Factor $- 1$ out of $- x$ .

$\frac{17 (- (x) + 8)}{18} = 0$

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{17 (- (x) - 1 (- 8))}{18} = 0$

Factor $- 1$ out of $- (x) - 1 (- 8)$ .

$\frac{17 (- (x - 8))}{18} = 0$

Simplify the expression.

Rewrite $- (x - 8)$ as $- 1 (x - 8)$ .

$\frac{17 (- 1 (x - 8))}{18} = 0$

Move the negative in front of the fraction.

$- \frac{17 (x - 8)}{18} = 0$

$- \frac{17 (x - 8)}{18} = 0$

$- \frac{17 (x - 8)}{18} = 0$

$- \frac{17 (x - 8)}{18} = 0$

Step 2

Set the numerator equal to zero.

$17 (x - 8) = 0$

Step 3

Solve the equation for $x$ .

Divide each term in $17 (x - 8) = 0$ by $17$ and simplify.

Divide each term in $17 (x - 8) = 0$ by $17$ .

$\frac{17 (x - 8)}{17} = \frac{0}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 (x - 8)}{17} = \frac{0}{17}$

Divide $x - 8$ by $1$ .

$x - 8 = \frac{0}{17}$

$x - 8 = \frac{0}{17}$

$x - 8 = \frac{0}{17}$

Simplify the right side.

Divide $0$ by $17$ .

$x - 8 = 0$

$x - 8 = 0$

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

$x = 8$

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